5.2 Unit circle: sine and cosine functions  (Page 8/12)

$\sin \frac{\pi }{2}$

$\sin \frac{\pi }{3}$

$\cos \frac{\pi }{2}$

$\cos \frac{\pi }{3}$

$\sin \frac{\pi }{4}$

$\cos \frac{\pi }{4}$

$\sin \frac{\pi }{6}$

$\sin \pi$

$\sin \frac{3\pi }{2}$

$\cos \pi$

$\cos 0$

$\cos \frac{\pi }{6}$

$\sin 0$

$\mathrm{240°}$

$-\mathrm{170°}$

$\mathrm{100°}$

$-\mathrm{315°}$

$\mathrm{135°}$

$\frac{5\pi }{4}$

$\frac{2\pi }{3}$

$\frac{5\pi }{6}$

$\frac{-11\pi }{3}$

$\frac{-7\pi }{4}$

$\frac{-\pi }{8}$

$\mathrm{225°}$

$\mathrm{300°}$

$\mathrm{320°}$

$\mathrm{135°}$

$\mathrm{210°}$

$\mathrm{120°}$

$\mathrm{250°}$

$\mathrm{150°}$

$\frac{5\pi }{4}$

$\frac{7\pi }{6}$

$\frac{5\pi }{3}$

$\frac{3\pi }{4}$

$\frac{4\pi }{3}$

$\frac{2\pi }{3}$

$\frac{5\pi }{6}$

$\frac{7\pi }{4}$

If $\text{cos}\left(t\right)=\frac{1}{7}$ and $t$ is in the 4 ^th quadrant, find $\text{sin}(t).$

If $\text{cos}\left(t\right)=\frac{2}{9}$ and $t$ is in the 1 ^st quadrant, find $\text{sin}(t).$

If $\text{sin}\left(t\right)=\frac{3}{8}$ and $t$ is in the 2 ^nd quadrant, find $\text{cos}(t).$

If $\text{sin}\left(t\right)=-\frac{1}{4}$ and $t$ is in the 3 ^rd quadrant, find $\text{cos}(t).$

Find the coordinates of the point on a circle with radius 15 corresponding to an angle of $\mathrm{220°}.$

Find the coordinates of the point on a circle with radius 20 corresponding to an angle of $\mathrm{120°}.$

Find the coordinates of the point on a circle with radius 8 corresponding to an angle of $\frac{7\pi }{4}.$

Find the coordinates of the point on a circle with radius 16 corresponding to an angle of $\frac{5\pi }{9}.$

State the domain of the sine and cosine functions.

State the range of the sine and cosine functions.

$\sin \frac{5\pi }{9}$

$\cos \frac{5\pi }{9}$

$\sin \frac{\pi }{10}$

$\cos \frac{\pi }{10}$

$\sin \frac{3\pi }{4}$

$\cos \frac{3\pi }{4}$

$\sin \mathrm{98°}$

$\cos \mathrm{98°}$

$\cos \mathrm{310°}$

$\sin \mathrm{310°}$

$\sin \left(\frac{11\pi }{3}\right)\cos \left(\frac{-5\pi }{6}\right)$

$\sin \left(\frac{3\pi }{4}\right)\cos \left(\frac{5\pi }{3}\right)$

$\sin \left(-\frac{4\pi }{3}\right)\cos \left(\frac{\pi }{2}\right)$

$\sin \left(\frac{-9\pi }{4}\right)\cos \left(\frac{-\pi }{6}\right)$

$\sin \left(\frac{\pi }{6}\right)\cos \left(\frac{-\pi }{3}\right)$

$\sin \left(\frac{7\pi }{4}\right)\cos \left(\frac{-2\pi }{3}\right)$

$\cos \left(\frac{5\pi }{6}\right)\cos \left(\frac{2\pi }{3}\right)$

$\cos \left(\frac{-\pi }{3}\right)\cos \left(\frac{\pi }{4}\right)$

$\sin \left(\frac{-5\pi }{4}\right)\sin \left(\frac{11\pi }{6}\right)$

$\sin \left(\pi \right)\sin \left(\frac{\pi }{6}\right)$

What are the coordinates of the child after 45 seconds?

What are the coordinates of the child after 90 seconds?

What is the coordinates of the child after 125 seconds?

When will the child have coordinates $\left(0.707,\mathrm{–0.707}\right)$ if the ride lasts 6 minutes? (There are multiple answers.)

When will the child have coordinates $(\mathrm{-0.866},\mathrm{-0.5})$ if the ride last 6 minutes?